Pharmacokinetics noncompartmental model

If one has pharmacokinetic data and knows that the situation calls for nonlinear kinetics, then compartmental models, no matter how difficult to postulate, are really required. Noncompartmental models cannot deal with the time-varying situation. 

This discussion will rely heavily on the following sources. First, the publications of DiStefano and Landaw (22, 23) deal with issues related to compartmental versus single accessible pool noncompartmental models. Second, Cobelli and Toffolo (3) discuss the two accessible pool noncompartmental model. Finally, Coveil et al. (4) provide the theory to demonstrate the link between noncompartmental and compartmental models in estimating the pharmacokinetic parameters. 

Suppose one has a set of pharmacokinetic data. The question is how to obtain information from the data related to the disposition of the drug in question. DiStefano and Landaw (22) deal with this question by making the distinction between models of data and models of system. Understanding this distinction is useful in understanding the differences between compartmental and noncompartmental models. 

As discussed, the noncompartmental model divides the system into two components an accessible pool and nonaccessible pools. The kinetics of the nonacces-sible pools are lumped into the recirculation-exchange arrows. From this, as has been discussed, we can estimate pharmacokinetic parameters describing the accessible pool and system. 

In conclusion, noncompartmental models and linear, constant-coefficient models have different domains of validity. When the domains are identical, then the pharmacokinetic parameters estimated by either method should, in theory, be equal. If they are not, then differences are due to the methods used to estimate them. 

There are three basic approaches to modeling pharmacokinetic data traditional compartmental models - (or classical modeling described in Chapters 1 and 12), noncompartmental models - (examined in this chapter), and physiologically based models. To understand when to use noncompartmental modeling, it is necessary to know the assumptions of each approach and the desired objective of the pharmacokinetic study. 

This approach has been incorrectly described as structureless pharmacokinetics, or model-independent pharmacokinetics. These references to noncompartmental modeling really are misnomers. This approach is not model-less instead, it uses a simpler, more general model. Another term used to describe this process is nonpara-metric pharmacokinetics because a structure with compartments and corresponding... 

The relative advantages and disadvantages of linear system analysis (LSA) and noncompartmentally based pharmacokinetic (PK) modeling to other modeling... 

The two most commonly used methods for characterizing pharmacokinetic data are noncompartmental analysis and the fitting of compartmental models. The latter technique can range from simple one to three well-stirred compartments to physiologically-based pharmacokinetic (PBPK) models, which are covered in the next section. The choice of which method to utilize will be largely dictated by the goals and objectives of the analysis. For example, descriptions of major pharmacokinetic parameters for linear systems (i.e., net systemic exposure is dose-proportional) can be easily calculated from a noncompartmental... 

Flooker, A.C., Foracchia, M., Dodds, M.G., and Vicini, P. 2003. An evaluation of population D-optimal designs via pharmacokinetic simulations. Ann. Biomed. Eng. 31 98-111. lacquez,l.A. 1996. Compartmental Analysis in Biology and Medicine. 3rded.,Biomedware,AnnArbor,MI. lacquez, l.A. and Simon, C.P. 1993. QuaUtative theory of compartmental systems. Siam. Rev., 35 43-79. Landaw, E.M. and DiStefano III, LI. 1984. Multiexponential, multicompartmental, and noncompartmental modeling. II. Data analysis and statistical considerations. Am. J. Physiol 246 R665-R677. 

Analysis of most (perhaps 65%) pharmacokinetic data from clinical trials starts and stops with noncompartmental analysis (NCA). NCA usually includes calculating the area under the curve (AUC) of concentration versus time, or under the first-moment curve (AUMC, from a graph of concentration multiplied by time versus time). Calculation of AUC and AUMC facilitates simple calculations for some standard pharmacokinetic parameters and collapses measurements made at several sampling times into a single number representing exposure. The approach makes few assumptions, has few parameters, and allows fairly rigorous statistical description of exposure and how it is affected by dose. An exposure response model may be created. With respect to descriptive dimensions these dose-exposure and exposure-response models... 

Two classical methods used in the analysis of pharmacokinetic data are the fitting of sums of exponential functions (2- and 3-compartment mammillary models) to plasma and/or tissue data, and less frequently, the fitting of arbitrary polynomial functions to the data (noncompartmental analysis). 

P. Veng-Pedersen. Noncompartmentally based pharmacokinetic modeling. Adv. Drug Deliv. Rev. 48 265-300, 2001. 

In contrast to noncompartmental analysis, in compartmental analysis a decision on the number of compartments must be made. For mAbs, the standard compartment model is illustrated in Fig. 3.11. It comprises two compartments, the central and peripheral compartment, with volumes VI and V2, respectively. Both compartments exchange antibody molecules with specific first-order rate constants. The input into (if IV infusion) and elimination from the central compartment are zero-order and first-order processes, respectively. Hence, this disposition model characterizes linear pharmacokinetics. For each compartment a differential equation describing the change in antibody amount per time can be established. For... 

Traditionally, linear pharmacokinetic analysis has used the n-compartment mammillary model to define drug disposition as a sum of exponentials, with the number of compartments being elucidated by the number of exponential terms. More recently, noncompartmental analysis has eliminated the need for defining the rate constants for these exponential terms (except for the terminal rate constant, Xz, in instances when extrapolation is necessary), allowing the determination of clearance (CL) and volume of distribution at steady-state (Vss) based on geometrically estimated Area Under the Curves (AUCs) and Area Under the Moment Curves (AUMCs). Numerous papers and texts have discussed the values and limitations of each method of analysis, with most concluding the choice of method resides in the richness of the data set. 

A basic assumption related to both methods of analysis is that the elimination of drug from the body is exclusively from the sampling compartment (i. e., blood/ plasma), and that rate constants are first order. However, when some or all of the elimination occurs outside the sampling compartment - that is, in the peripheral or tissue compartment(s) - these types of analysis are prone to error in the estimation of Vss, but not CL. In compartmental modeling, the error is related to the fact that no longer do the exponents accurately reflect the inter-compartmental and elimination (micro) rate constants. This model mis specification will result in an error that is related to the relative magnitudes of the distribution rate constants and the peripheral elimination rate constant. However, less widely understood is the fact that this model mis specification will also result in errors in noncompartmental pharmacokinetic analysis. 

From previous chapters it is clear that the evaluation. of pharmacokinetic parameters is an essential part of understanding how drugs function in the body. To estimate these parameters studies are undertaken in which transient data are collected. These studies can be conducted in animals at the preclinical level, through all stages of clinical trials, and can be data rich or sparse. No matter what the situation, there must be some common means by which to communicate the results of the experiments. Pharmacokinetic parameters serve this purpose. Thus, in the field of pharmacokinetics, the definitions and formulas for the parameters must be agreed upon, and the methods used to calculate them understood. This understanding includes assumptions and domains of validity, for the utility of the parameter values depends upon them. This chapter focuses on the assumptions and domains of validity for the two commonly used methods — noncompartmental and compartmental analysis. Compartmental models have been presented in earlier chapters. This chapter expands upon this, and presents a comparison of the two methods. 

The pharmacokinetic parameters descriptive of the system are as follows (although these definitions apply to both noncompartmental and compartmental models, some modification will be needed for two accessible pool models as well as compartmental models) ... 

Gillespie WR. Noncompartmental versus compart-mental modeling in clinical pharmacokinetics. Clin Pharmacokinet 1991 20 253-62. 

One of the most common transformations is the natural logarithmic transformation of multiplicative models. Many pharmacokinetic parameters, such as area under the curve (AUC) and maximal concentration, are log-normal in distribution (Lacey et al., 1997), and hence, using the Ln-transformation results in approximate normality. The rationale is as follows (Westlake, 1988). For a drug that has linear kinetics and elimination occurs from the central compartment (the usual assumptions for a noncompartmental analysis) then... 

Hence, intravenous data were modeled first, followed by inhalational, then intranasal. Once the pharmacokinetics of each individual route of administration was established, all model parameters were then estimated simultaneously. Initial values for cocaine pharmacokinetics after intravenous administration were estimated using noncompartmental methods. Total systemic clearance was estimated at 100 L/h and volume of distribution at steady-state was estimated at 232 L. Central compartment clearance and intercompartmental clearance were set equal to one-half total systemic clearance (50 L/h), whereas central and peripheral compartment volumes were set equal to one-half volume of distribution (116 L). Data were weighed using a constant coefficient of variation error model based on model-predicted plasma concentrations. All models were fit using SAAM II (SAAM Institute, Seattle, WA). An Information-Theoretic approach was used for model selection, i.e., model selection was based on the AIC. 

The study of pharmacokinetics may be pursued at a number of levels. Considering the detail of the mathematical models involved one may use a noncompartmental, classical, or physiologically based approach. All three approaches require some measure of mathematical description or assumptions with the classical, compartmental approach intermediate in complexity. This chapter describes the development and use of compartmental models in pharmacokinetic research. Noncompartmental and physiologically based pharmacokinetic models are discussed in Chapters 13 and 14, respectively. 

Gillespie, W. R., Noncompartmental versus compartmental modeling in clinical pharmacokinetics, Clin. Pharmacokinet., 20 253-262, 1991. 

Various pharmacokinetic parameters such as CL, Vd, F%, MRT, and im can be determined using noncompartmental methods. These methods are based on the empirical determination of AUC and AUMC described above. Unlike compartmental models (see below), these calculation methods can be applied to any other models, provided that the drug follows linear pharmacokinetics. However, a limitation of the noncompartmental method is that it cannot be used for the simulation n of different plasma concentration-time profiles when there are alterations in dosing regimen or when multiple dosing regimens are used. 

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